Step 1: Prepare the Pickle-Brined Carrots (Optional, but Recommended). In a small bowl, combine the dill pickle brine and water. Add the peeled and chopped carrots to the brine. Let them sit at room temperature while you prepare the other components, or refrigerate for up to a few hours.

Step 2: Preheat Oven and Prepare Pan. Preheat the oven to 350°F (175°C), with the rack in the center of the oven. Grease a metal 13×9-inch pan with nonstick baking spray. Line the pan with a piece of parchment paper, leaving an overhang on two sides for easy removal later. Lightly grease the parchment paper with nonstick baking spray as well.

Step 3: Cook the Carrots. Fill a medium pot with 1 inch of water and place a steamer basket inside. Cover the pot and bring the water to a boil over high heat. Drain the carrots from the brine, and add them to the steamer basket. Reduce the heat to low, cover the pot, and steam until the carrots are very tender, 20 to 25 minutes.

Step 4: Make the Carrot Puree. While the carrots are still hot, transfer them to a small bowl with the 2 tablespoons of butter. Using an immersion blender or food processor, puree until smooth. Set aside to cool (you should have about 1 cup of carrot puree).

Step 5: Make the Carrot Cake Batter (Dry Ingredients). In a medium bowl, whisk together the flour, baking powder, cinnamon, cardamom, and cloves.

Step 6: Brown the Butter. Place a large saucepan over medium heat and add 12 tablespoons (1 ½ sticks) of the butter. Let it melt, then continue to cook, swirling the pan occasionally, until the butter is golden brown and has a nutty aroma, 5 to 6 minutes.

Step 7: Finish Butter Mixture. Remove the pan from the heat and add the remaining 4 tablespoons of butter. Swirl the pan continuously until the butter stops foaming, then whisk in the brown sugar, vanilla extract, and salt.

Step 8: Cool Butter Mixture. Transfer the brown butter-sugar mixture to a large bowl and let it cool to room temperature, about 30 minutes.

Step 9: Make the Cream Cheese Batter. While the butter mixture is cooling, make the cream cheese batter. Add the cream cheese to a medium bowl. If it is not soft enough to whisk, microwave in 10-second intervals until it is softened but not melted. Whisk in the sour cream, granulated sugar, vanilla extract, egg and dill pickle powder until there are no lumps. Set aside.

Step 10: Combine Wet and Dry Ingredients. Once the brown butter-sugar mixture is cool, whisk in the cooled carrot puree until you have a smooth mixture. Add the eggs and yolks all at once and whisk together until fully combined. Add the dry ingredients and stir until just combined, then add the pecans, gently folding them into the batter.

Step 11: Assemble the Bars. Spread half of the carrot cake batter into the prepared pan. Using half of the cream cheese mixture, dollop tablespoonfuls on top of the carrot cake batter and swirl it through with a butter knife or wooden skewer.

Step 12: Add Remaining Layers. Gently spread the remaining carrot cake batter over the top, aiming to cover most of the cream cheese (it does not have to be perfect). Dollop the remaining cream cheese mixture over the top and repeat the swirling process. Don’t be afraid to really go for it so that you evenly distribute the cream cheese mixture and there’s some in every bite!

Step 13: Bake. Bake until the cream cheese swirl has set and a toothpick inserted into the center of the bars comes out with only a few crumbs attached, 30 to 35 minutes.

Step 14: Cool and Cut. Remove from the oven and transfer to a wire rack to cool completely. Use the parchment paper overhang to lift the cake out of the pan and cut into bars.

Step 15: Serve (Optional Garnish). Sprinkle with finely chopped fresh dill (optional) Serve immediately or store in the fridge until ready to serve. Serve with dill pickle relish on the side, if desired.